Question

word problem attached, please help!!

Answer 1

Nice picture @retirEEd

Answer 2

I mean profile picture

Answer 3

This question stumped me for way too long of a time. I can only think it is getting to late or I am getting too old. Let's see if a can explain it

He travels 4060 miles into a 6 mph headwind in x hours
he returns 4060 miles with a 6 mph tailwind in x-12 hours

[4060/(x-12) + 6] = [(4060/x) -6]
[4060/(x-12)] - [(4060/x)] = - 6 -6

Now it is just algebra that I can't seemed to able to do tonight. I don't know why.

so I will just give you the answers that seem to work

70 mph with the wind
58 mph into the wind

64 with no wind These answers seem way too low for an airplane, but I think they are correct. Check the work yourself. I need to get to bed.

Answer 4

\[d=st\]\[d=4060\]\(s\) is speed of aircraft in still air, so flying into headwind of 6 mph, we have a speed of \(s-6\), and flying with the wind, we have a speed of \(s+6\)

flying against the wind:

\[4060=(s-6)t\]flying with the wind:\[4060=(s+6)(t-12)\]

both of those have the same left hand side, so we can equate them:
\[(s-6)t = (s+6)(t-12)\]expanding:
\[st-6t=st-12s+6t-72\]simplifying:\[st-st-6t=st-st-12s+6t-72\]\[-6t-6t=-12s+6t-6t-72\]\[-12t=-12s+72\]divide through by \(-12\) and we have \[t=s+6\]
This doesn't seem all that helpful, except we know we can find the values of \(s\) and \(t\) :

\[(s-6)t=4060\]substitute expression for \(t\) in terms of \(s\)
\[(s-6)(s+6)=4060\]\[s^2-36=4060\]\[s^2=4096\]\[s=64\](we can disregard the negative solution here, as the plane is not flying backwards)

So, to check our solution:

\[t=s-6 = 64+6=70\]
flying against wind, \[(64-6)(70) = 58*70=4060\checkmark\]flying with the wind,\[(64+6)(70-12) = 70*58=4060\checkmark\]

Answer 5

Thanks for explaining that to me.

Reviewing my work, I did manage to get x = s - 6, where x = time, but I couldn't figure out what to do with it.